The complex Radon correspondence relates an n-dimensional projective space with the Grassmarm manifold of its p-dimensional planes. This is the geometric background of the Radon–Penrose transform, which intertwines cohomology classes of homogeneous line bundles with holomorphic solutions to the generalized massless field equations. A good framework to deal with such problems is provided by the recently developed theory of integral transforms for sheaves and D-modules. In particular, an adjunction formula describes the range of transforms acting on general function spaces, associated with constructible sheaves.
The linear group SL(n + 1,C) naturally acts on the Radon correspondence. A distinguished family of function spaces is then the one associated with locally constant sheaves along the closed orbits of the real forms of SL(n + 1,C). In this paper, we systematically apply the above-mentioned adjunction formula to such function spaces. We thus obtain in a unified manner several results concerning the complex, conformal, or real Radon transforms.
Cite this article
Andrea D'Agnolo, Corrado Marastoni, Real Forms of the Radon–Penrose Transform. Publ. Res. Inst. Math. Sci. 36 (2000), no. 3, pp. 337–383